Quartic del Pezzo surfaces without quadratic points
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909635170009088 |
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| author | Creutz, Brendan Viray, Bianca |
| author_facet | Creutz, Brendan Viray, Bianca |
| contents | Previous work of the authors showed that every quartic del Pezzo surface over a number field has index dividing $2$ (i.e., has a closed point of degree $2$ modulo $4$),, and asked whether such surfaces always have a closed point of degree $2$. We resolve this by constructing infinitely many quartic del Pezzo surfaces over $\mathbb{Q}$ without degree $2$ points. These are the first examples of smooth intersections of two quadrics with index strictly less than the minimal degree of a closed point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08436 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quartic del Pezzo surfaces without quadratic points Creutz, Brendan Viray, Bianca Number Theory Algebraic Geometry 14G05, 14G12 Previous work of the authors showed that every quartic del Pezzo surface over a number field has index dividing $2$ (i.e., has a closed point of degree $2$ modulo $4$),, and asked whether such surfaces always have a closed point of degree $2$. We resolve this by constructing infinitely many quartic del Pezzo surfaces over $\mathbb{Q}$ without degree $2$ points. These are the first examples of smooth intersections of two quadrics with index strictly less than the minimal degree of a closed point. |
| title | Quartic del Pezzo surfaces without quadratic points |
| topic | Number Theory Algebraic Geometry 14G05, 14G12 |
| url | https://arxiv.org/abs/2408.08436 |